# Algebraic Surfaces and Holomorphic Vector Bundles

@inproceedings{Friedman1998AlgebraicSA, title={Algebraic Surfaces and Holomorphic Vector Bundles}, author={Robert Friedman}, year={1998} }

1 Curves on a Surface.- Invariants of a surface.- Divisors on a surface.- Adjunction and arithmetic genus.- The Riemann-Roch formula.- Algebraic proof of the Hodge index theorem.- Ample and nef divisors.- Exercises.- 2 Coherent Sheaves.- What is a coherent sheaf?.- A rapid review of Chern classes for projective varieties.- Rank 2 bundles and sub-line bundles.- Elementary modifications.- Singularities of coherent sheaves.- Torsion free and reflexive sheaves.- Double covers.- Appendix: some…

## 362 Citations

### Ju n 20 03 Stable bundles on non-Kähler elliptic surfaces

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In this paper, we study the moduli spaces Mδ,c2 of stable rank-2 vector bundles on non-Kähler elliptic surfaces. Such a surface X admits a holomorphic fibration without a section, whose general fibre…

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- Mathematics
- 2011

Consider a simply connected, smooth, projective, complex surface X. Let Mfk(X) be the moduli space of framed irreducible anti-self-dual connections on a principal SU(2)-bundle over X with second…

### Moduli of rank 2 Higgs sheaves on elliptic surfaces

- MathematicsGeometriae Dedicata
- 2022

We study torsion-free, rank 2 Higgs sheaves on genus one fibered surfaces, (semi)stable with respect to suitable polarizations in the sense of Friedman and O’Grady. We prove that slope-semistability…

### A NOTE ON RANK TWO STABLE BUNDLES OVER SURFACES

- MathematicsGlasgow Mathematical Journal
- 2021

Abstract. Let π : X → C be a fibration with integral fibers over a curve C and consider a polarization H on the surface X. Let E be a stable vector bundle of rank 2 on C. We prove that the pullback…

### Stability in Categories and Normal Projective Varieties over Perfect Fields

- Mathematics
- 2020

We present a notion of ∆-stability and stability filtration in arbitrary categories which is equivalent to the existence of Harder-Narasimhan (HN) sequences on objects. Indeed it is equivalent to the…

### Stability of rank 2 vector bundles along isomonodromic deformations

- Mathematics
- 2009

We are interested in the stability of holomorphic rank 2 vector bundles of degree 0 over compact Riemann surfaces, which are provided with irreducible meromophic tracefree connections. In the case of…

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- MathematicsTransactions of the American Mathematical Society
- 2018

Rational curves on Hilbert schemes of points on
K
3
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surfaces and generalised Kummer manifolds are constructed by using Brill–Noether theory on nodal curves on the underlying…

### Lectures on K3 Surfaces

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Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular and each chapter ends with questions and open problems.

### Geometric and Spectral Analysis

- Mathematics
- 2014

A new proof of a Bismut-Zhang formula for some class of representations by M. Braverman and B. Vertman Tunneling, the Quillen metric and analytic torsion for high powers of a holomorphic line bundle…